We derive an asymptotic lower bound for the correlation and generalized correlations of proximate factors with the population factors providing guidance on how to construct the proximate factors.
From (1.3), (1.4), and Theorem 3.1 we clearly see that (M_{2/3}(a,b)) is the sharp upper power mean bound for the 2-order generalized logarithmic mean (L^{1/2}(a^{2}, b^{2})), the first Seiffert mean (P a,b)), and the second Yang mean (V a,b)).
Next, we prove that L 4 ( a, b ) is the best possible lower generalized logarithmic mean bound for the Neuman-Sándor mean M ( a, b ).
Next, we prove that L 5 ( a, b ) is the best possible lower generalized logarithmic mean bound for the second Seiffert mean T ( a, b ).
holds for all a, b > 0 with a ≠ b, and L 5 ( a, b ) is the best possible lower generalized logarithmic mean bound for the second Seiffert mean T ( a, b ).
holds for all a, b > 0 with a ≠ b, and L 4 ( a, b ) is the best possible lower generalized logarithmic mean bound for the Neuman-Sándor mean M ( a, b ).
With the help of Lemma 3.1, new upper bound for the right-hand side of (1.6) for generalized ((alpha,m -preinvex functions vialpha,m -preinvexville functionsl integral is presented in the following theorem.
Also shown for comparison are the following: an inner bound using binary DPC alone, or the generalized DPC with and ; and the inner bound for the capacity region of the case in which the state is known to neither the encoders nor the decoder.
We derived an inner bound for the DM case and specialized to a noiseless binary case using generalized binary DPC.
